Acta mathematica scientia,Series A ›› 2001, Vol. 21 ›› Issue (4): 559-569.
• Articles • Previous Articles Next Articles
DING Yi-Ming, FAN Wen-Tao
Online:
Published:
Supported by:
国家自然科学基金资助项目(19847005,69874039)
Abstract:
该文研究一簇Lorenz映射犛犪:[0,1]→[0,1](0<犪<1)犛犪(狓)=狓+犪 狓∈ [0,1-犪){(狓+犪-1)/犪 狓∈ [1-犪,1].从拓扑的角度考虑了犛犪的混沌行为,证明了:犛犪有稠密轨道;犛犪的周期的集合犘犘(犛犪)={1,犿+1,犿+2,…},其中犿为使犪犿<1-犪成立的最小正整数;犛犪的拓扑熵犺(犛犪)>0;几乎所有(关于Lebesgue测度)的点狓的Lyapunov指数λ(犛犪,狓)=λ犪>0.从统计的角度讨论了犛犪的稳定性.我们用下界函数方法证明了犛犪是统计稳定的,并且狌犵犪(犃)=∫犃犵犪(狓)d狓(犃∈犅)为犛犪的唯一绝对连续(关于Lebesgue测度)不变概率测度.同时,不变密度犵犪在参数扰动和随机作用的随机扰动下是稳定的.
Key words: Lorenz映射, 混沌, FrobeniusPerron算子, 不变密度, 统计稳定, 参数扰动, 随机作用的随机扰动
CLC Number:
DING Yi-Ming, FAN Wen-Tao. The Chaotic Behavior and Statistically Stable Behaviour of a Family of Lorenz Maps[J].Acta mathematica scientia,Series A, 2001, 21(4): 559-569.
0 / / Recommend
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
URL: http://121.43.60.238/sxwlxbA/EN/
http://121.43.60.238/sxwlxbA/EN/Y2001/V21/I4/559
1 毕桥.子动力学理论及其在复杂动力系统中的应用.武汉:武汉工业大学出版社,1998 2 丁玖,周爱辉.不变测度及其计算.数学进展,1998,27:309-323 3 LasotaA,Mackey M.Chaosfractalsandnoise.AppliedMathematicalSciences97,2ndEd.Berlin:SpringerVerlag, 1994 4 GlendinningP,Sparrow C.Primeandrenormalisablekneadinginvariantsandthedynamicsofexpanding Lorenz maps.PhysicaD,1993,62:22-50 5 KeenerJ.Chaoticbehaviorinpiecewisecontinuousdifferenceequations.TransAmerMathSoc,1980,261:589-604 6 Malkin MI.RotationintervalsandthedynamicsofLorenztypemappings.SelectaMathematicaSovietica,1991,10: 265-275 7 AlsedàL,LlibreJ,MisiurewiczM,TresserC.PeriodsandentropyforLorenzlikemaps.AnnInstFourier,Greno ble,1989,39:929-952. 8 DingYiming,Fan Wentao.AsymptoticperiodicityofLorenzmaps.ActaMathematicaScientia,1999,1:114-120 9 VianaM.Dynamics:Aprobabilisticandgeometricperspective.DocumentaMathematica,ExtraVolumeICM1998,1 -22 10 GóraP,BoyarskyA.Anewapproachtocontrollingchaoticsystems.PhysicaD,1998,111:1-15 11 BiQiao,AntoniouI.SpectraldecompositionofChebyshevmaps.PhysicaA,1996,233:449-457
Cited
The Flow-capturing Location-allocation Model with Risk Bottleneck Limitation